A nonlinear creep model of rocks based on memory-dependent derivative

Abstract

The creep behavior of soil and rock exhibits significant time-dependence and non-linearity, which are difficult to capture using traditional composite element models. In the framework of memory-dependent derivative theory, a memory-dependent visco-pot element with non-linear creep behavior, no instantaneous deformation, elastic after-effect, and stress relaxation is proposed. By connecting a memory-dependent visco-pot element with strain triggering to the Nishihara model, a memory-dependent derivative creep model is developed and its constitutive equation is derived. The creep test data pertaining to coal, salt, sandstone, and olivine rock are used to validate the model, which can describe the initial creep, steady-state creep, and non-linear accelerated creep deformation characteristics of various soil and rock materials. Comparison with fractional-order models, improved Nishihara models, and Hehai models shows that our model has better fitting results and is more advantageous in characterizing the non-linear features of soil and rock during the accelerated creep stage.